Consider the following L$.$P$.$P$.$:

Max. $Z=4x_1+10x_2$

subject to constraints:

$2x_1+x_2{a}_1$

$2x_1+5x_2{a}_2$

$2x_1+3x_2{a}_3$

$x_1,x_{2}0$

where $a_1,a_2$ and $a_3$ are constants. For specific values

of $a_1,a_2$ and $a_3$ the optimal solution is :

Evaluate the following :

$($i$)$ The values of $a_1,a_2$ and $a_3$ that yield the given

optimal solution.

$($ii$)$ The values of $b_1,b_2$ and $b_3,d$ and $e$ in the above

given optimal table.